Related papers: One-generated nilpotent assosymmetric algebras
We give a classification of $5$- and $6$-dimensional complex one-generated nilpotent bicommutative algebras.
We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras
We give an algebraic classification of complex $5$-dimensional one-generated nilpotent terminal algebras.
We give a complete description of degenerations of complex $5$-dimensional nilpotent associative commutative algebras.
This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.
The paper is devoted to give a complete classification of five-dimension nilpotent evolution algebras over an algebraically closed field. We obtained a list of 27 isolated non-isomorphic nilpotent evolution algebras and 2 families of…
This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller…
This paper is devoted to the complete algebraic classification of complex 5-dimensional nilpotent bicommutative algebras.
We give a geometric classification of complex $n$-dimensional $2$-step nilpotent (all, commutative and anticommutative) algebras. Namely, has been found the number of irreducible components and their dimensions. As a corollary, we have a…
We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…
We give algebraic and geometric classifications of $6$-dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are $14$ one-parameter families of $6$-dimensional nilpotent anticommutative…
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
We give an algebraic classification of complex $4$-dimensional nilpotent $\mathfrak{CD}$-algebras.
We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb C$ from both algebraic and geometric approaches.
In this paper we give the complete classification of $5$-dimensional complex solvable symmetric Leibniz algebras.
We give a complete description of degenerations of $3$-dimensional nilpotent algebras, $4$-dimensional nilpotent commutative algebras and $5$-dimensional nilpotent anticommutative algebras over $ \mathbb C$. In particular, we correct…
We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.
We give a geometric classification of all $6$-dimensional nilpotent Tortkara algebras over $\mathbb C$
An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.
In this paper we classify filiform associative algebras of degree $k$ over a field of characteristic zero. Moreover, we also classify naturally graded complex filiform and quasi-filiform nilpotent associative algebras which are described by…